Explicit construction of a Chern-Moser connection for CR manifolds of codimension two
Abstract
In the present paper we suggest an explicit construction of a Cartan connection for an elliptic or hyperbolic CR manifold M of dimension six and codimension two, i.e. a pair (P, w), consisting of a principal bundle P over M and of a Cartan connection form w on P, satisfying the following property: the (local) CR transformations of M are in one to one correspondence with the (local) automorphisms of P which preserve w. For any point x in M, this construction determines an explicit immersion of the stability subalgebra Lie(aut(M)_x) into the Lie algebra Lie(H) of the structure group H of P.
Cite
@article{arxiv.math/0209036,
title = {Explicit construction of a Chern-Moser connection for CR manifolds of codimension two},
author = {Gerd Schmalz and Andrea Spiro},
journal= {arXiv preprint arXiv:math/0209036},
year = {2007}
}
Comments
40 pages - This is a revised version in which a misuse of formula (6.10) of the old version in the following computations has been corrected - the changes starts only from pag. 24 and do not concerns the line of arguments